> > I was just reacting to the notion that the integers as a whole
> are "simpler"
> > than individual large integers. While this statement reflects a deep
> > mathematical fact, it's also a bit of a play on words, as the
> mathematical
> > notion of simplicity involved is somewhat counterintuitive, and
> it not the
> > only interesting mathematical notion fo simplicity...
>
> But, continuing through from the original thread of discussion, my point
> is that assuming the existence of other universes can render the
> description "simpler" in that sense which Occam's Razor requires.

yeah... I think I see the point ... but I'm still not sure I like it!

As I understand it, the point is that assuming the existence of *all
possible finite universes* consistent with observed reality may well be
simpler than assuming the existence of *some particular* finite universe
consistent with observed reality...

If one views this in terms of Kolmogorov complexity, then one says: The
program to generate all possible finite universes consistent with observed
reality may be very short, whereas the program to generate some particular
finite universe consistent with observed reality may be long due to
requiring a lot of details.... (This relates to Juergen Schmidhuber's ideas
on "God as a Programmer")

Note, however, that the story becomes different if one includes runtime in
one's assessment of program complexity (instead of just program length as in
Kolmogorov complexity). The program that iterates through all possible
universes is pretty slow, compared to the one that generates some particular
possible universe in all its details.

So, the practical application of occam's razor here seems to depend upon the
details.... Which is the point at which we transition from speculative
philosophy to speculative physics, I suppose.